Negative thermal expansion in YbMn[subscript 2]Ge[subscript 2] induced by the dual effect of magneti
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Qiao, Yongqiang↗
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New Tunable Negative Thermal Expansion Ceramics in Polymer Composites.
Abstract not provided.
Gordon, Margaret Ellen↗
Transforming Thermal Expansion from Positive to Negative: The Case of Cubic Magnetic Compounds of (Zr,Nb)Fe 2
Negative thermal expansion (NTE) is an intriguing property for not only fundamental studies but also technological applications. However, few NTE materials are available compared with the huge amount of positive thermal expansion materials. The discovery of new NTE materials remains challenging. In this paper, we report a chemical modification strategy to transform thermal expansion from positive to negative in cubic magnetic compounds of (Zr,Nb)Fe 2 by tuning the magnetic exchange interaction. Furthermore, an isotropic zero thermal expansion can be established in Zr 0.8 Nb 0.2 Fe 2 (α 1 = 1.4 x 10 -6 K -1 , 3-470 K) over a broad temperature range that is even wider than that of the prototype Invar alloy of Fe 0.64 Ni 0.36 . The NTE of (Zr,Nb)Fe 2 is originated from the weakened magnetic exchange interaction and the increased d electrons of Fe by the Nb chemical substitution, so that the magnetovolume effect overwhelms the contribution of anharmonic lattice vibration.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Processing, structure, and thermal properties of ZrW 2 O 8 , HfW 2 O 8 , HfMgW 3 O 12 , Al(HfMg) 0.5 W 3 O 12 , and Al 0.5 Sc 1.5 W 3 O 12 negative and zero thermal expansion coefficient ceramics
Negative and zero coefficient of thermal expansion (CTE) materials are of interest for developing polymer composites in electronic circuits that match the expansion of Si and in zero CTE supports for optical components, e.g., mirrors. In this work, the processing challenges and stability of ZrW 2 O 8 , HfW 2 O 8 , HfMgW 3 O 12 , Al(HfMg) 0.5 W 3 O 12 , and Al 0.5 Sc 1.5 W 3 O 12 negative and zero thermal expansion coefficient ceramics are discussed. Al 0.5 Sc 1.5 W 3 O 12 is demonstrated to be a relatively simple oxide to fabricate in large quantity and is shown to exhibit single phase up to 1300 °C in air and inert N 2 environments. The negative and zero CTE behavior was confirmed with dilatometry. Thermal conductivity and heat capacity were reported for the first time for HfMgW 3 O 12 and Al 0.5 Sc 1.5 W 3 O 12 and thermal conductivity was found to be very low (~0.5 W/mK). Grüneisen parameter is also estimated. Methods for integration of Al 0.5 Sc 1.5 W 3 O 12 with other materials was examined and embedding 50 vol% of the ceramic powder in flexible epoxy was demonstrated with a commercial vendor.
36 MATERIALS SCIENCE↗
Tunable negative coefficient thermal expansion materials and composites
The present disclosure is directed to variable composition ceramics. Zr (2−x) Hf (x) WP 2 O 12 and Hf 2 WP 2 O 12 exhibit large negative thermal expansion that is linear over a large temperature range up to at least 900° C., These new ceramic material particles may be mixed with polymers to make a composite suitable for use in backsheets for photovoltaic modules or in other applications. The thermal expansion coefficient of the composite can be tailored to match that of the solar cell in order to reduce stress resulting from daily thermal cycling.
Gordon, Margaret Ellen↗
Computation of the Thermal Expansion Coefficient of Graphene with Gaussian Approximation Potentials
Direct experimental measurement of thermal expansion coefficient without substrate effects is a challenging task for two-dimensional (2D) materials, and its accurate estimation with large-scale ab initio molecular dynamics is computationally very expensive. Machine learning-based interatomic potentials trained with ab initio data have been successfully used in molecular dynamics simulations to decrease the computational cost without compromising the accuracy. In this work, we investigated using Gaussian approximation potentials to reproduce the density functional theory-level accuracy for graphene within both lattice dynamical and molecular dynamical methods, and to extend their applicability to larger length and time scales. Two such potentials are considered, GAP17 and GAP20. GAP17, which was trained with pristine graphene structures, is found to give closer results to density functional theory calculations at different scales. Further vibrational and structural analyses verify that the same conclusions can be deduced with density functional theory level in terms of the reasoning of the thermal expansion behavior, and the negative thermal expansion behavior is associated with long-range out-of-plane phonon vibrations. Thus, it is argued that the enabled larger system sizes by machine learning potentials may even enhance the accuracy compared to small-size-limited ab initio molecular dynamics.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Structural changes upon magnetic ordering in magnetocaloric AlFe 2 B 2
With a Curie temperature just above room temperature, AlFe 2 B 2 is a useful magnetocaloric material composed of earth-abundant elements. Here, we employ temperature-dependent high-resolution synchrotron X-ray diffraction to establish with high certainty that the paramagnetic to ferromagnetic transition in AlFe 2 B 2 is of second order, showing no discontinuity in lattice parameters or cell volume. Nevertheless, the lattice parameters undergo anisotropic changes across the transition with distinct differences in the thermal expansion coefficients. While the $a$ and $b$ lattice parameters show a positive thermal expansion, $c$ shows a negative thermal expansion. We link these changes to the respective interatomic distances to determine the contribution of magnetism to the anisotropic structural evolution. The work underpins the possible role of magnetostructural coupling in driving the magnetocaloric effect in AlFe 2 B 2 .
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Mechanical and Thermal Properties for Uranium and U–6Nb Alloy from First-Principles Theory
Elasticity, lattice dynamics, and thermal expansion for uranium and U–6Nb alloy (elastic moduli) are calculated from density functional theory that is extended to include orbital polarization (DFT+OP). Introducing 12.5 at.% of niobium, substitutionally, in uranium softens all the cii elastic moduli, resulting in a significantly softer shear modulus (G). Combined with a nearly invariant bulk modulus (B), the quotient B/G increases dramatically for U–6Nb, suggesting a more ductile material. Lattice dynamics from a harmonic model coupled with a DFT+OP electronic structure is applied for α uranium, and the obtained phonon density of states compares well with inelastic neutron-scattering measurements. The Debye temperature associated with the lattice dynamics falls within the range of experimentally observed Debye temperatures and it also validates our quasi-harmonic (QH) phonon model. The QH Debye–Grüneisen phonon method is combined with a DFT+OP electronic structure and used to explore the anisotropic thermal expansion in α uranium. The anomalous negative thermal expansion (contraction) of the b lattice parameter of the α-phase orthorhombic cell is relatively well reproduced from a free-energy model consisting of QH-phonon and DFT+OP electronic structure contributions.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Anharmonic phonons, thermal expansion, and nuclear quantum effects in Zn
The anharmonic behavior of phonons and thermal expansion of hexagonal zinc were studied from 15 to 690 K by inelastic neutron scattering (INS) and ab initio simulations. Phonon spectra were measured for Q-points covering the full Brillouin zone, giving the phonon density of states (DOS) and dispersions along high-symmetry directions. The dispersions were sharp at 15 K, but diffuse intensity was observed at energies above them. The dispersions broadened with temperature T and the diffuse intensity became stronger. This diffuse intensity appeared in all INS measurements and simulations, except for classical molecular dynamics at 15 K. The temperature-dependent effective potential (TDEP) method, which included the nuclear quantum effect from zero-point vibrational dynamics, was used to calculate the free energy and thermal expansion. For T < 100 K nuclear quantum effects were important for obtaining the correct negative thermal expansion, and path integral molecular dynamics (PIMD) was particularly effective for obtaining the negative thermal expansion in the basal plane. A Heisenberg-Langevin model for interacting phonons coupled to a thermal bath was able to reproduce the shape and intensity of the diffuse spectral features.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Zentropy theory for accurate prediction of free energy, volume, and thermal expansion without fitting parameters
Based on statistical mechanics, a macroscopically homogeneous system, i.e., a single phase in the present context, is composed of many independent configurations that the system embraces. The macroscopical properties of the system are determined by the properties and statistical probabilities of those configurations with respect to external conditions. The volume of a single phase is thus the weighted sum of the volumes of all configurations. Consequently, the derivative of the volume to temperature of a single phase depends on both the derivatives of the volumes of every configuration to temperature and the derivatives of their statistical probabilities to temperature, with the latter introducing nonlinear emergent behaviors. It is shown that the derivative of the volume to the temperature of the single phase can be negative, i.e., negative thermal expansion, due to the symmetry-breaking non-ground-state configurations with smaller volumes than that of the ground-state configuration and the rapid increase of the statistical probabilities of the former, and negative thermal expansion can be predicted without fitting parameters from the zentropy theory that combines quantum mechanics and statistical mechanics with the free energy of each configuration predicted from quantum mechanics and the partition function of each configuration calculated from its free energy.
36 MATERIALS SCIENCE↗
Elucidating the local structure of Li 1+ x Al x Ti 2– x (PO 4 ) 3 and Li 3 Al x Ti 2– x (PO 4 ) 3 ( x = 0, 0.3) via total scattering
Li 1+x Al x Ti 2–x (PO 4 ) 3 (LATP) and Li 3 Al x Ti 2–x (PO 4 ) 3 (x = 0, 0.3) are promising candidates in all-solid-state batteries due to their high room temperature conductivity of 10 –3 S cm –1 and air- and moisture-stability. They also exhibit unusual thermal expansion properties, with Li 1+x Al x Ti 2–x (PO 4 ) 3 showing near-zero thermal expansion along the a axis while Li 3 Al x Ti 2–x (PO 4 ) 3 exhibits polynomial positive thermal expansion along the a axis and polynomial negative thermal expansion along the c axis. A crucial component to understanding these properties is understanding the local structure. Total scattering is a powerful analytical technique as it provides information on the long-range, average structure as well as the local structure. Here, we report the first X-ray and neutron total scattering experiments performed on Li 1+x Al x Ti 2–x (PO 4 ) 3 and Li 3 Al x Ti 2–x (PO 4 ) 3 (x = 0, 0.3). We show that the PO 4 and TiO 6 polyhedra experience very little expansion of the P/Ti–O bonds up to 800 °C, nor is there much expansion when the Li content increases significantly. The minor thermal expansion of the nearest-neighbor bonds of the polyhedra is revealed to be the reason behind the unusual thermal expansion properties, causing the near-zero thermal expansion along a in Li 1+x Al x Ti 2–x (PO 4 ) 3 and moving as whole units in Li 3 Al x Ti 2–x (PO 4 ) 3 . The structural robustness of the framework is also the reason for the increased conductivity as Li content increases, as the framework remains undistorted as Li content increases, permitting Li-ion mobility as the number of charge carriers increases. Finally, this suggests that phosphate-based framework materials beyond LATP would also be a good material space to explore for new Li-ion (and other ion-) conducting materials.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Hybrid Double Perovskite Containing Helium: [He 2 ][CaZr]F 6
Perovskites are of great technological and geological importance, in large part, due to their considerable compositional and structural flexibility. However, the formation of perovskites with neutral species on their A-sites is very unusual. The formation, phase transitions and properties of [He 2 ][CaZr]F 6 , which is the first noble gas containing perovskite to be made, are reported. It is likely that a large family of related materials can also be prepared. On compression in neon, the negative thermal expansion (NTE) material CaZrF 6 amorphizes at ~ 0. 5 GPa. However, on compression in helium at room temperature, gas is inserted into the structure to form a perovskite with helium on the A-site. This suppresses the amorphization until > 3 GPa. Volume versus pressure and Raman measurements suggest that filling of the A-site, to give [He 2 ][CaZr]F 6 , is complete at > 1 GPa. The presence of helium on the A-site in this perovskite leads to a reduction in the magnitude of negative thermal expansion when compared to the parent phase CaZrF 6 , likely due to steric impediment of the transverse vibrational motion of fluoride. The helium also leads to considerable stiffening of the structure. At room temperature and ~2.5 GPa, the helium containing hybrid perovskite has a bulk modulus of ~ 47 GPa, whereas CaZrF 6 has a bulk modulus of ~ 40 GPa at ambient. At 15 K, the cubic perovskite [He 2 ][CaZr]F 6 undergoes a structural phase transition, that likely involves a cooperative tilting of framework octahedra to give a lower-symmetry phase, which is tentatively assigned as tetragonal.
36 MATERIALS SCIENCE↗
Surviving nanoscale interfacial stability in extreme thermal expansion contrast Zn(CN) 2 -epoxy resin matrix composites
Here, we report the remarkable stability at the nanoscale matrix-filler interface in a series of overall low coefficient of thermal expansion (CTE) zinc cyanide (ZC)/epoxy resin composites. These interfaces demonstrate the stability of highly contrasting materials. These composites are designed to optimize the properties of both materials: epoxy resins are valued for their high strength, superb chemical resistance, low dielectric properties, and adhesive abilities. ZC, a model flexible framework, exhibits negative thermal expansion (NTE) behavior and compensates for the epoxy resin’s detrimentally large thermal expansion values. Filled resins minimize the native 65 ppm/°C CTE values to 19 ppm/° C over a wide temperature range while maintaining linearity, yielding composites compatible with typical metal and ceramic substrates’—commonly bonded to the resin— 0–20 ppm/° C CTE values. Additionally, with significant intrinsic differences in the materials, we use wide-angle X-ray diffraction and atomic force microscopy to elucidate thermal movement. The ZC/epoxy interface is surprisingly resilient over 1,000 cycles between -55° C and 75° C, extremes typical to aerospace applications. Further, we show that the resin viscosity remains less than 21 Pa*s at up to 30 vol% ZC, an important consideration for workability. We also discuss settling distribution, glass transition temperature, flexural strength, and longevity. All results point favorably towards practical implementation in low thermal expansion application needs: filling the gap in component design.
42 ENGINEERING↗
First principles free energy model with dynamic magnetism for δ -plutonium
We present an ab initio free energy model derived from a fully relativistic density functional theory (DFT) electronic structure with dynamic magnetism for δ -plutonium (face-centered cubic, fcc). The DFT model is extended with orbital-orbital interaction in a parameter free orbital polarization (OP) mechanism consistent with previous modeling of plutonium. Gibbs free energy is built from components associated with the temperature dependence of the electronic structure and the corresponding electronic entropy, lattice vibrations within an anharmonic lattice dynamics model, and dynamical fluctuations of the magnetization density, i.e. magnetic fluctuations. The fluctuation model consists of transverse and longitudinal modes driven by temperature induced excitations of the DFT + OP electronic structure. The ab initio model thus incorporates fluctuating states beyond the electronic ground state. Thanks to the dynamic magnetism, the theory predicts excellent thermodynamic properties and a Gibbs free energy in accord with CALPHAD and semi-empirical modeling developed from the thermodynamic observables. The magnetic fluctuations further explain anomalous behaviors of the thermal expansion in plutonium. Specifically, a thermal expansion for the δ -plutonium system turning from positive to negative at temperatures above room temperature, a tendency for gallium to reduce and remove the negative thermal expansion depending on composition, and a positive thermal expansion for the high temperature ϵ phase.
dynamic↗
ZENN: A thermodynamics-inspired computational framework for heterogeneous data–driven modeling
Traditional entropy-based methods—such as cross-entropy loss in classification problems—have long been essential tools for representing the information uncertainty and physical disorder in data and for developing artificial intelligence algorithms. However, the rapid growth of data across various domains has introduced new challenges, particularly the integration of heterogeneous datasets with intrinsic disparities. To address this, we introduce a zentropy-enhanced neural network (ZENN), extending zentropy theory into the data science domain via intrinsic entropy, enabling more effective learning from heterogeneous data sources. ZENN simultaneously learns both energy and intrinsic entropy components, capturing the underlying structure of multisource data. To support this, we redesign the neural network architecture to better reflect the intrinsic properties and variability inherent in diverse datasets. We demonstrate the effectiveness of ZENN on classification tasks and energy landscape reconstructions, showing its superior generalization capabilities and robustness-particularly in predicting high-order derivatives. In image and text classification tasks, ZENN demonstrates superior generalization by introducing a learnable temperature variable that models latent multisource heterogeneity, allowing it to surpass state-of-the-art models on CIFAR-10/100, BBC News, and AG News. As a practical application in materials science, we employ ZENN to reconstruct the Helmholtz energy landscape of Fe3Pt using data generated from density functional theory and capture key material behaviors, including negative thermal expansion and the critical point in the temperature–pressure space. Overall, this work presents a zentropy-grounded framework for data-driven machine learning, positioning ZENN as a versatile and robust approach for scientific problems involving complex, heterogeneous datasets.
36 MATERIALS SCIENCE↗
Negative and zero thermal expansion in α-(Cu 2-x Znx)V 2 O 7 solid solutions
Negative or zero thermal expansion (NTE or ZTE) of materials is intriguing for controllable thermal expansion. In this work, we report a series of orthorhombic α-Cu 2- x Zn x V 2 O 7 ( x = 0, 0.1, 0.2), in which the volumetric coefficients of thermal expansion are successfully tuned from -10.19 × 10 -6 K -1 to -1.58 × 10 -6 K -1 in the temperature range of 100–475 K by increasing the content of Zn 2+ . It has been revealed that the transverse vibrations of oxygen bonded with vanadium are dominant in the contraction of the bc plane, leading to the overall volume NTE in α-Cu 2 V 2 O 7 . The introduction of Zn 2+ densifies the crystal structure, which is presumed to suppress the space of transverse vibrations and results in the ZTE in α-Cu 1.8 Zn 0.2 V 2 O 7 . This work presents an effective method to realize ZTE in anisotropic framework systems.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗